A pressurized oil supplied from an oil pump is used to control the switching or lock-up of an automatic transmission in a vehicle. A rotation speed of the oil pump which is necessary to maintain an oil pressure (line pressure) to the minimum value is determined from the supply response characteristics of the oil pressure and the characteristics of the transmission. As a result, the rotation speed of the pump can not fall below a fixed rotation speed.
However when the vehicle is in a state in which the next speed ratio control step is not immediately performed, for example when the brake pedal is depressed bringing the vehicle to a halt, it may be the case that the required line pressure will fall below the minimum line pressure as discussed above. Thus even in this situation, the oil pump rotation speed is held above a fixed value in order to maintain the fixed minimum line pressure. However the maintenance of a minimum line pressure in the above situation is not effective from the point of view of energy consumption. Furthermore the problem of reducing pump operation noise has arisen.